Critical long-range percolation

It is conjectured that many models of statistical mechanics have a rich, fractal-like behaviour at and near their points of phase transition, with power-law scaling governed by critical exponents that are expected to depend on the dimension but not on the small-scale details of the model such as the choice of lattice. This is now reasonably well understood in two dimensions and in high dimensions, but remains poorly understood in intermediate dimensions (e.g. d=3).  I will describe a new technique for studying models with long-range interactions which leads to some striking new results some of which have surprisingly easy proofs.

Tom Hutchcroft received his PhD from UBC in 2017 under the supervision of Asaf Nachmias and Omer Angel. After four years as a postdoc in Cambridge, he became a Professor of Mathematics at Caltech in 2021. His UBC PhD thesis was awarded the Governor General's Gold Medal and the doctoral prize of the Canadian Mathematical Society.